Elliptic curve isogeny class 60.1-e over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-60.1-e
• Conductor: 60.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{15}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 15 \); class number \(2\).

Elliptic curves in class 60.1-e over \(\Q(\sqrt{15}) \)

Isogeny class 60.1-e contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
60.1-e1	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -3 a + 1\) , \( -2 a + 2\bigr] \)
60.1-e2	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 2 a - 19\) , \( 15 a - 64\bigr] \)
60.1-e3	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 332 a - 1309\) , \( 7257 a - 28138\bigr] \)
60.1-e4	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 17 a - 89\) , \( 140 a - 574\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 6 & 3 \\ 2 & 1 & 3 & 6 \\ 6 & 3 & 1 & 2 \\ 3 & 6 & 2 & 1 \end{array}\right)\)

Isogeny graph